UNIT A2
Recommended Prior Knowledge Units A1, N1.
Context The ideas of order of operations and brackets are formally introduced, for both number and algebra.
Outline Having established the order of operations, brackets are then used with linear expressions and equations in algebra.
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Learning Outcomes
Use the four operations including correct
ordering of operations and use of
brackets
Suggested Teaching Activities
Talk about the meaning of e.g. 4 + 3 × 2
and establish with students the correct
order of operations and the need to use
brackets to do (4 + 3) × 2. Similarly the
solution of division problems where there is
more than one term in the numerator or
denominator. Give the students practice in
using their calculators efficiently to solve
such problems, as well as those which they
should do without a calculator.
Use brackets and extract common
factors; expand products of the form a(bx
+ cy); factorise expressions of the form
ax + ay
Show students the meaning of 6(x + 2y) by
expanding the brackets. Give them
practice in expanding and simplifying linear
expressions such as 3x + 5(x + y) − 2(5x −
4y). Factorise expressions such as 4a +
6b.
Move on to solving harder linear equations
than in unit A1. Include equations involving
brackets such as 4(2x + 1) = 16 and also
equations where the unknown appears on
both sides, such as 4x + 3 = 2x − 5.
Resources
http://www.ex.ac.uk/cimt/mepres/allgcse/bka6.pdf has
work on using brackets and memory on a calculator at
section 6.6
http://www.ex.ac.uk/cimt/mepres/allgcse/bkb10.pdf has
questions of suitable difficulty in section 10.5
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UNIT D2
Recommended Prior Knowledge Unit D1
Context This unit moves on from individual data to representing and calculating with simple frequency distributions for discrete data.
Outline This unit includes constructing and interpreting bar charts, pie charts and pictograms. The mean of a discrete frequency distribution is calculated, in
preparation for D3, where grouped continuous data will be used.
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Learning Outcomes
Collect, classify and tabulate discrete
data. Read, interpret and draw simple
inferences from tables and statistical
diagrams
Construct and use bar charts, pie charts,
pictograms.
Suggested Teaching Activities
Look at a chart of each type which has
been drawn already. For each one, ask
questions about the information which has
been shown. Draw attention to the title,
labels on axes / bars / sectors and to the
key for a pictogram. Ask which is the mode
for each diagram. Ask ‘How many...?’ for
each diagram, ensuring that students then
realise that a pie chart does not show this,
just relative proportions.
Get the students to collect some data of
their own, tabulate it and represent it. For
instance, in preparation for probability work
in D4, they could undertake experiments
with a biased die or spinner and tabulate
the resulting frequencies for each number.
Or you may wish them to undertake a
survey. As well as drawing diagrams by
hand, if one or more computers are
available teach them to use a computer
program such as Excel or Autograph to
represent data.
[Calculate the mean of a discrete
frequency distribution.]
Resources
Two worksheets on interpreting athletics data are available
at http://www.ex.ac.uk/cimt/resource/dint1.htm and
http://www.ex.ac.uk/cimt/resource/dint2.htm, with a link to the
data file.
If you do not have printed charts that you can show, you
could draw them yourself on Excel, perhaps using an extract
of data from http://www.censusatschool.ntu.ac.uk/
There are some examples at
http://www.ex.ac.uk/cimt/mepres/allgcse/bkb8.pdf.
http://www.xist.org/ has global and regional statistics e.g. the
populations for different districts in a country and also has
charts.
Give the students a list of data with
repeats, say 30 items, and ask them to
calculate the mean. Whilst they do this, put
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the data into a frequency distribution on the
board and add an extra column. Then
show them how to get their result using the
frequency distribution. Then for the next
example, just give the data in the form of a
frequency distribution and ask them to
calculate the mean.
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UNIT N2
Recommended Prior Knowledge Unit N1.
Context Integers were studied in unit N1. This unit involves fractions and decimals and so completes the basis of working with different types of real number.
As with N1, much of this work may be familiar to some students, and so the time taken by the unit will depend on the level at which the class is already.
Outline The concepts of fractions, decimals and percentages and conversions between them are established. The four operations of working with fractions
and decimals are used. Percentages of a quantity are found. These number skills are then applied to money and personal finance problems.
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Learning Outcomes
Use the language and notation of simple
vulgar and decimal fractions and
percentages in appropriate contexts;
recognise equivalence and convert
between these forms.
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Use rational and irrational numbers.
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Use the four operations for calculations
with decimal fractions and vulgar (and
mixed) fractions.
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Calculate a given percentage of a
quantity; express one quantity as a
percentage of another, calculate
percentage increase or decrease.
Suggested Teaching Activities
Revise the concepts of equivalence e.g.
asking how 0.8 might be expressed
differently. Give students practice in
simplifying fractions and in converting
between fractions, decimals and
percentages. Include the fact that all
terminating and recurring decimals may be
expressed as fractions and so are rational,
and that non-recurring decimals are
irrational.
Check the students’ level of competence in
the four operations with fractions and
decimals. Give appropriate teaching and
practice.
Begin by asking orally for 50% of 200g,
10% of $50 etc and progress to formal
methods of finding a percentage of a
quantity. Similarly use questions such as
‘What fraction of 40 cm is 8 cm?’ to
progress to expressing one quantity as a
percentage of another.
Resources
http://www.mathsnet.net/fractions/index.html gives some
fractions practice, and gives solutions
http://www.ex.ac.uk/cimt/mepres/allgcse/bka6.pdf has
exercises and worked examples for decimals,
http://www.ex.ac.uk/cimt/mepres/allgcse/bkb11.pdf deals
with fractions after percentages.
http://www.ex.ac.uk/cimt/mepres/allgcse/bkb11.pdf covers
this work.
Calculate percentage increase and
decrease, using contexts such as length,
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Solve problems involving money and
convert from one currency to another.
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Use given data to solve problems on
personal and household finance involving
earnings, simple interest, discount, profit
and loss; extract data from tables and
charts
time or mass as well as money (see also
below).
Use the context of shopping to set money
problems, giving students practice in
solving them without a calculator, as well
as with one when the difficulty is
appropriate. Use conversions between
currencies, using conversion graphs as
well as conversion rates.
Currency conversions are at http://finance.yahoo.com/m3?u
Use local tax rates for goods and wages and other local
contexts for personal finance
Mail-order catalogues and order forms are another good
source of data.
Calculate simple interest, discounts, profit
and loss. Calculate earnings and solve
other personal and household finance
problems, including using tables and charts
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UNIT S2
Recommended Prior Knowledge Unit N1, S1.
Context This unit could be studied before S1 if wished, by introducing the units for area here. Much of this unit should already be familiar to students, so
check their knowledge and move forward at an appropriate pace.
Outline This unit concerns lines and angles, triangles and quadrilaterals. The basic geometrical terms associated with them are introduced and unknown
angles are calculated using angle properties. Triangles and quadrilaterals are classified, including the symmetry properties of different types. Areas of
triangles, rectangles and parallelograms are calculated.
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Learning Outcomes
Use and interpret the geometrical terms:
point, line, plane, parallel, perpendicular,
right angle, acute, obtuse and reflex
angles.
Use and interpret vocabulary of triangles,
special quadrilaterals.
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Recognise line and rotational symmetry
(including order of rotational symmetry)
in two dimensions and properties of
triangles and quadrilaterals directly
related to their symmetries.
Calculate unknown angles and give
simple explanations using the following
geometrical properties:
(a) angles on a straight line
(b) angles at a point
(c) vertically opposite angles
(d) angles formed by parallel lines
(e) angle properties of triangles and
quadrilaterals
Solve problems involving
(i) the perimeter and area of a rectangle
Suggested Teaching Activities
Students could be reminded of this
terminology by showing them a picture of a
pattern such as a tiled floor using different
shapes and asking them to identify an
obtuse angle, a kite, perpendicular lines etc
Resources
For instance there are geometrical patterns, including a
gallery of pictures of artworks at
http://www.salaam.co.uk/themeofthemonth/march02_index.
php?l=3
Show students pictures of shapes and
logos which have line or rotational
symmetry and ask them to identify how
many lines of symmetry the shape has and
what its order of rotational symmetry is.
Move on to the symmetry properties of
isosceles and equilateral triangles and
special quadrilaterals.
The class could make a poster showing the
angle and symmetry properties of special
triangles and quadrilaterals.
http://www.ex.ac.uk/cimt/mepres/allgcse/bka3.pdf has
useful work on symmetry as well as angles
Make sure the students know the angle
properties (a) to (d) then move on to solve
angle problems for each of types (a) to (e),
asking the students to give their reasons
for each calculation.
It may be helpful to show students how the
area formulae for a parallelogram and a
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/sy
mmetryrev2.shtml has interactive demonstrations and
information about symmetry
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/an
glesrev2.shtml has clear diagrams
http://www.ex.ac.uk/cimt/mepres/allgcse/bka3.pdf has
plenty of examples and exercise
http://www.ex.ac.uk/cimt/mepres/allgcse/bkb7.pdf has work
on the area and perimeter of squares, rectangles and
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and triangle
(ii) the area of a parallelogram and a
trapezium
trapezium may be obtained by splitting
them into two triangles. After this,
encourage them to work with the area
formulae. Give them practice in finding
areas and perimeters, making sure that
they give the appropriate units in their
answers.
triangles at section 7.6.
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